New extended (3+1)-dimensional KP-type equations: Painlevé integrability, multi-solitons, and lump solutions

This work investigates and analyzes two new extended (3+1)-dimensional Kadomtsev-Petviashvili (KP) equations describing nonlinear wave propagation in dissipative media such as fluid mechanics and plasmas. The Painleve test is conducted to explore the necessary conditions to justify the integrability test for both models. Using the simplified Hirota method, we derive the dispersion relations, multiple soliton solutions, and associated phase shifts after interaction for each equation. The first three soliton solutions of every equation are derived and then graphically investigated to grasp their propagation dynamics. Furthermore, we use the bilinear form of the extended KP equations to explore a class of lump solutions for these equations using distinct parameters values.